Therefore a quadratic function can be written in vertex form as
y = a(x - h)^2 + k.
Define quadratic function.In mathematics, a polynomial of degree two in one or more variables is referred to as a quadratic polynomial. The polynomial function that a quadratic polynomial defines is known as a quadratic function.
What is a polynomial function?In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.
A quadratic function can be written in vertex form as y = a(x - h)^2 + k
Where (h, k) is the vertex, and a is the leading coefficient.
y = ax^2 + bx + c (standard form)
y = a(x + b/2a)^2 + c - b^2/4a
y = a(x - h)^2 + k where h = -b/2a and k = c - b^2/4a
For example,when y = 3x^2 - 6x - 5
y = 3x^2 - 6x - 5
y = 3(x^2 - 2x) - 5
y = 3(x^2 - 2x + 1 - 1) - 5 = 3(x - 1)^2 - 8
So, the equation is in vertex form y = 3(x - 1)^2 - 8
Note that this only works for parabolas that opens upwards or downwards, if the parabola opens to the sides, the vertex form is y = a(x-h)^2 +k
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Write the equation of the perpendicular bisector’s of the line AB given: A(1,3) & B(-3,5)
Answer:
y = 2x + 1
Step-by-step explanation:
[tex]\frac{5-3}{-3-1}[/tex] = [tex]\frac{2}{-4}[/tex] = [tex]\frac{1}{-2}[/tex]
Perpendicular slopes are the opposite reciprocals . So the slope of the line will be 2
slope (m) = 2
y = 3 You could use either point given. I chose (1,3)
x = 1 From the point given (1,3)
y = mx + b substitute in what you know and solve for b
3 = (2)(1) + b
3 = 2 + b Subtract 2 from both sides
1 = b
The y-intercept is 1.
y = mx + b
y = 2x + 1
To arrive at his appointment on time, Mr. Jones needs to drive from his home at the average speed of 60 mph. But traffic is heavy, so Mr. Jones drives 15 mph slower than planned and arrives at the appointment 20 minutes late. How many miles from his home is the appointment
On solving the provided question, we can say that by equation 60 miles from his home is the appointment
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
for d and t
60 = d/t
45 = d / t + 0.33
60t = d
45( t + 0.33) = d
60t = 45t + 15
t = 1 hour
d = 60 X 1 miles = 60 mile
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5. Katie has 15/20 of a dollar in her pocket. Lisa has the same amount of money in
her pocket. What fraction of a dollar does Lisa have in her pocket?
A. 5/10 B. 3/4
C. 4/5 D. 2/10
Answer:
Step-by-step explanation:
it B.
just put in the calculator and it gives you the reduced fraction
Answer:
B. 3/4
Step-by-step explanation:
Find the GCD (or HCF) of the numerator and denominator
GCD of 15 and 20 is 5
Next, divide both the numerator and denominator by the GCD
15 ÷ 5 = 3
20 ÷ 5 = 4
Finally, put them back into a fraction
[tex]\frac{3}{4}[/tex]
Therefore, 15/20 simplified to the lowest terms is 3/4.
Find the unit rate of the constant of proportionality for the following: $9.80 for 5 pounds.
Showing your work would be appreciated, so if you could, that’d be great. But it’s not needed, if you don’t want to. :)
Thank you in advance to anyone who answers!
The unit rate of constant means that for every 1 pound, the output is 1.96 dollar.
What is proportionality?Proportionality is a relationship between two variables in which their ratio is always equal to a constant value. In mathematical terms, it can be expressed as y = kx, where y and x are the two variables, and k is the constant of proportionality.
What is rate?A rate is a measure of how one quantity changes in relation to another quantity. It is usually expressed as a ratio and has units of measurement, such as miles per hour, dollars per pound, etc. A unit rate is a rate in which the second quantity is one unit of measurement.
The unit rate of the constant of proportionality is found by dividing the change in y (output) by the change in x (input).
In this case:
$9.8/5$ = $1.96$, so the unit rate of the constant of proportionality is 1.96 pounds/dollar.
It means that for every 1 pound, the output is 1.96 dollar.
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A sector of a circle has an area of 55cm if the radius is 10cm calculate the angle of the sector
Answer:
Step-by-step explanation:
the ans is in the picture with the steps
(hope it helps can i plz have brainlist :D hehe)
Kaj and her children went into a grocery store and she bought $8 worth of apples and bananas. Each apple costs $1 and each banana costs $0.50. She bought 2 more apples than bananas. By following the steps below, determine the number of apples, x,x, and the number of bananas, y,y, that Kaj bought.
Kaj bought 3 bananas and 5 apples.
Finding the numbers of apples and bananas using substitution method.To determine the number of apples and bananas that Kaj bought, we can set up a system of equations.We know that the total amount spent on apples and bananas is $8.We know that each apple costs $1 and each banana costs $0.50.We know that Kaj bought 2 more apples than bananas.From these three pieces of information, we can set up the following two equations:
x + y = 8 (The total number of apples and bananas is 8)x + 0.5y = 8 (The total amount spent is $8)x = y + 2 (Kaj bought 2 more apples than bananas)We can substitute the third equation into the first equation and get:
y+2 + y = 8
So we know that y = 3
Now we can substitute this value into the second equation and get:
x + 0.5(3) = 8
So we know that x = 5
So Kaj bought 3 bananas and 5 apples.
And also we can substitute y = 3 into the third equation and get:
x = y + 2
So we know that x = 5
So Kaj bought 3 bananas and 5 apples.
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What is the greatest common factor (GCF) of this expression?
Answer:
B
Step-by-step explanation:
A swimming pool is a shape of a rectangular prism. The pool is 10 feet deep. It length is 3 times it's width. The volume of the pool is 27000 cubic feet. Find the length and the width of the pool.
Answer:
Step-by-step explanation:
V = l * w * h
27000ft3 = (2w) * w * 10ft
27000ft3 = 2w^2 * 10ft
2700 = 2w^2
1350 = w^2
W = 36.74
*PLEASE HELP ASAP!!!*
Therefore Because of this, the square root is 2 is "irrational" (cannot be written as a fraction) since, if it were, the result would be absurd.
What is the square root?A mathematical concept known as a square root is indeed a factor of a number that, when multiplied on its own, equal the original value. For instance, 3 and -3 are the cube roots of 9. Starting in the second millennium BC, the Babylonians created effective methods for approximating square roots.
Here,
In this case, The square root of 2 is "irrational" (cannot be expressed in a fraction) because, if It Could,
You Would Have the Nonsensical Situation That The Fraction Would Have Even Integer value
At Both The Top And Bottom And Could Therefore Always Be Simplified.
.
Therefore Because of this, the square root is 2 is "irrational" (cannot be written as a fraction) since, if it were, the result would be absurd.
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would this be sin, cos, or tan?
Answer:
cos
Step-by-step explanation:
its adjacent over hypotenuse
Answer: cos
Step-by-step explanation:
You don't have a value for the side opposite the angle, you only have your hypotenuse and your adjacent side. Hope this helps.
Avery types a 42 word paragraph in 2/3 minute. What is her typing speed in words per
minute.
help !
Answer:
Step-by-ste63p explanation:
2/3 = 42
1/3 = 42 ÷ 2
=21
3/3 is 1 min
3/3 = 21 x 3
= 63
PLEASE HELP GIVING BRAINLIESTTTTTT
Simplify the expreion. The expreion negative one fifth j plu three fourth minu the expreion five halve j plu even eighth negative 27 over 10 time j plu negative 1 over 8 27 over 10 time j plu 1 over 8 negative 23 over 10 time j minu 13 over 8 negative 23 over 10 time j plu 13 over 8
The simplified value of the given expression ⇒ [(-1 / 5 j) + (3 / 4) - 5 / 2j - (7 / 8)] is computed at ⇒ [(-27 / 10 j) - (1/ 5)]
An algebraic expression is one that was created in mathematics by using integer variables, constants, and algebraic operations.
However, since they are not produced by using integer constants and algebraic operations, transcendental numbers like such and e are not algebraic. The production of is commonly stated as a geometric expression, although the definition of e requires an infinite number of algebraic operations. An expression can be reduced to a rational fraction by using the properties of arithmetic operations.
You can write the given expression as:
⇒ (-1 / 5 j) + 3 / 4 - 5 / 2j - 7 / 8
When we simplify the formula and apply the fractional operations to the result, we get:
⇒ (-27 / 10 j) - (1/ 5)
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Please help due today:///
Answer:
No solutions mean that the graphs don't intersect. There are two of them in this collection.
WILL SEND 90$ NEED HELP ON ALGERBA 1 PROBLEMS PLEASE HELP
OK. What? First off- what does "will send 90$ mean"? Second- Where and or what are these "Algebra 1 Problems" you speak of?
BTW- if u meant 90 dollars, the dollar sign goes before not after the number: $90. Just saying.
Find the measure of the third side. Round your answer to the nearest whole number.
Sabrina rode on a Ferris wheel at the state fair. The radius of the Ferris wheel was 106 feet. What is the approximate distance Sabrina traveled in one revolution of the Ferris wheel? (Use 3.14 for T.)
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Answer:
666 ft
Step-by-step explanation:
The circumference of the wheel is given by the formula ...
C = 2πr
For a radius of 106 ft, the circumference is ...
C = 2(3.14)(106 ft) = 665.68 ft
Sabrina traveled about 666 feet in one revolution.
Please help me! Will mark brainliest if you show steps
Amahl does computer repairs in his home. He charges a set fee to analyze the problem, plus an hourly rate for his labor. The table below shows C, the total charge to his customer, based on H, the number of hours of labor required.
Which equation could amahl use to determine his customer's total charge?
A. C = 9h + 21
B. C = 12h + 15
C. C = 15h + 9
D. C + 24h + 15
Answer:
definitely equation B
steps:
multiply 12 by the hours, and add 15. for each part, it will equal the total charge. 12*2+15 and so on. hope this helps
What is the degree of the polynomial of 5x²y 8xy² 9?
The polynomial is a mathematical expression containing variables and coefficients and can be written as a sum of terms of various degrees. In this case, the polynomial is composed of three terms of varying degrees: 5x²y, 8xy² and 9. The degree of this polynomial is the highest degree of the terms, which is 4.
1. Identify the terms of the polynomial: 5x²y, 8xy² and 9
2. Identify the degree of each term: 5x²y has degree 3, 8xy² has degree 4 and 9 has degree 0
3. Determine the highest degree among the terms: The highest degree is 4
4. The degree of the polynomial is then the highest degree among the terms, which is 4.
A polynomial is a mathematical expression consisting of variables and coefficients and can be written as a sum of terms of varying degrees. In this case, the polynomial consists of three terms: 5x²y, 8xy² and 9. To determine the degree of the polynomial, we must first identify the degree of each term. The term 5x²y has degree 3, the term 8xy² has degree 4 and the term 9 has degree 0. The degree of the polynomial is then the highest degree among the terms, which is 4. This means that the polynomial has a degree of 4, as the highest degree among its terms is 4. The degree of a polynomial is an important factor in solving equations and other mathematical problems, as it can determine the complexity of the equation.
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A "Pick 2" lottery game involves drawing 2 numbered balls from separate bins each containing balls labeled from 0 to 9. So there are 100 possible selections in total: 00, 01, 02, ..., 98, 99. Players can choose to play a "straight" bet, where the player wins if they choose both digits in the correct order. Since there are 100 possible selections, the probability a player wins a straight bet is 1/100. The lottery pays $50 on a successful $1 straight bet, so a player's net gain if they win this bet is $49. Let X represent a player's net gain on a $1 straight bet. Calculate the expected net gain E(X). Hint: The expected net gain can be negative. E(X) = dollars
The expected net gain E(X) in the context of this problem is given as follows:
E(X) = -$0.5.
How to obtain the expected net gain?The net gain for this problem is modeled for a discrete distribution, as there are only two possible outcomes, given as follows:
Winning $49.Losing $1.The probability of winning is of 1% = 0.01, while the probability of losing is of 99% = 0.99, hence the distribution of gains for this problem is given as follows:
P(X = -1) = 0.99.P(X = 49) = 0.01.The expected value of a discrete distribution is calculated as the sum of each outcome multiplied by it's respective probability.
Hence the expected net gain for this game is calculated as follows:
E(X) = -1 x 0.99 + 49 x 0.01.
E(X) = -$0.5.
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hello please help i’ll give brainliest
Answer:
d
Step-by-step explanation:
Answer:
the third one
Step-by-step explanation:
The Earth is in a constant state of change. Earth’s crust, called the lithosphere, consists of 15 to 20 moving tectonic plates. The plates can be thought of like pieces of a cracked shell that rest on the hot, molten rock of Earth’s mantle and fit snugly against one another. The heat from radioactive processes within the planet’s interior causes the plates to move, sometimes toward and sometimes away from each other. This movement is called plate motion, or tectonic shift.
Our planet looks very different from the way it did 250 million years ago, when there was only one continent, called Pangaea, and one ocean, called Panthalassa. As Earth’s mantle heated and cooled over many millennia, the outer crust broke up and commenced the plate motion that continues today.
The huge continent eventually broke apart, creating new and ever-changing land masses and oceans. Have you ever noticed how the east coast of South America looks like it would fit neatly into the west coast of Africa? That’s because it did, millions of years before tectonic shift separated the two great continents.
Earth’s land masses move toward and away from each other at an average rate of about 0.6 inch a year. That’s about the rate that human toenails grow! Some regions, such as coastal California, move quite fast in geological terms — almost two inches a year — relative to the more stable interior of the continental United States. At the “seams” where tectonic plates come in contact, the crustal rocks may grind violently against each other, causing earthquakes and volcano eruptions. The relatively fast movement of the tectonic plates under California explains the frequent earthquakes that occur there.
Please help.. what am I missing on this?
A. 78
B. 12.75
C. 136.5
D. 12
Answer:
A. 78
Step-by-step explanation:
You want the measure of one base angle of an isosceles triangle when it is given as (6x+6)° while angle K is given as 2x°.
Angle relationsYou don't need to solve any equations to determine the correct answer choice. You just need to understand the relationship between angles in an isosceles triangle.
The two base angles in an isosceles triangle are congruent, so neither can be more than 90°. (Eliminates choice C.)
The base angle at (6x+6) is more than 3 times angle K at (2x), so the base angle cannot be as little as 12.75. (Eliminates choices B and D.)
The only viable answer choice is A. 78°.
SolutionThe sum of angles in any triangle is 180°. The two base angles in an isosceles triangle are the same measure, so we have ...
(6x +6)° +(6x +6)° +2x° = 180°
14x +12 = 180 . . . . . . . . . . . divide by °, collect terms
14x = 168 . . . . . . . . . . subtract 12
x = 12 . . . . . . . . . . divide by 14
∠D = (6x +6)° = (6·12 +6)° = 78°
__
Additional comments
We are referring to the angle marked 2x° as "angle K" because Brainly doesn't like the word a.pex to show up in an answer.
We know triangle DKT is isosceles because the sides are marked with a single hash mark. The congruent base angles are opposite the congruent sides.
An altitude from K to segment DT would divide the triangle into two congruent right triangles, each with its half of angle K being x°. Then angles K/2 and T are complementary to that, so you could write ...
6x +6 +x = 90 ⇒ 7x = 84 ⇒ x = 12 ⇒ ∠D = 90° -12° = 78°
Once again, recognition that 6x+6 is somewhat greater than x means that angle D must be somewhat more than 45°. (The larger of two things is always greater than half their sum.)
A water sprinkler sends water out in a circular pattern. How large is the watered area if the radius of the watering pattern is 21 ft?
Answer:
1386 ft^2
Step-by-step explanation:
Area of a circle = πr²
Where : = π = pi = 22/7
R = radius
22/7 x 21^2 = 1386 ft^2
Using the measure of x. What is the measure of ∠AMB?
Answer:
∠AMB = 54°
Step-by-step explanation:
2x + (x + 9) = 90°
3x + 9° = 90°
3x = 81°
x = 27°
∠AMB = 2x = 54°
Answer:
angle AMB is 54
Step-by-step explanation:
2x+ x+9= 90
simplify and get 27
I put 90 in RHS Because The total equals to 90.
if you want to check your work, Do this-
we have the value of x which is 27
so substitute the values and angle AMB will be 54.
Angle BMC will be 36
add them and should get 90.
The Garcia family bought 400 yards of fencing to enclose a circular wildflower garden. They will use all of the fencing whats the area
The area of the windflower garden that is enclosed by a circular fence of 400 yards length is equal to 12732.39 square yards.
What is circumference of a circle?The measurement of the circle's perimeter, also known as its circumference, is called the circle's border. It is the length around the border of the circular object or the circle itself.
What is the formula for calculating the perimeter of a circle?The formula for calculating the perimeter of a circle is ,
Perimeter/ Circumference of a circle = 2 * pi * r, where pi = 3.14 and r is the radius of the circle.
Taking the given information in the question, i.e circumference of the circular fencing wire , i.e C = 400 yards
or , 2 * pi * r = 400
or , r = 400/(2* 3.14)
r = 63.66 yards
Now the area of the circular fence is given by,
Area = pi * r^2
Area = 3.14 * 63.66^2
Area = 12732.39 square yards
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Given the exponential function, f ( x ) = 4 ( .75 ) x .
What is the asymptote for this function?
1 - y = 0
2. y = 4
3. x = 4
4. x = 0
Answer:
Answer 1
Step-by-step explanation:
Sorry I'm very busy so no step by step
Cornelio creates a tree diagram to show all possibilities for flipping a coin four times.How many possibilities are in the sample space at the end of the tree diagram
A 4
B 5
C 8
D 16
Option D is correct, there are 16 possibilities are in the sample space at the end of the tree diagram
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given that Cornelio creates a tree diagram to show all possibilities for flipping a coin four times
We need to find the number of possibilities are in the sample space at the end of the tree diagram
The number of times coin is flipped=4
We can use 2ⁿ to figure out the number of possible outcomes where n is the number of tosses.
Now n=4, so the number of possibilities are 2⁴
2×2×2×2
16
Hence, option D is correct, there are 16 possibilities are in the sample space at the end of the tree diagram
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The figure oelow is a composite of a
semicircle and a trapezoid.
9 cm
4 cm
5 cm
Which measurement is closest to the area
of the composite figure?
A 91.6 cm? C 68.4 cm?
B 78.2 cm? D 83.6 cm?
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Answer:
C 68.4 cm²
Step-by-step explanation:
The area of the semicircle is given by ...
A = 1/2π(d/2)^2 = (π/8)d^2
A = (π/8)(9 cm)^2 ≈ 31.8 cm^2
The area of the trapezoid is given by ...
A = 1/2(b1 +b2)h
A = 1/2(9 cm + 5 cm)(4 cm) = 28 cm^2
Then the total area is ...
31.8 cm^2 +28 cm^2 = 59.8 cm^2
Of the offered choices, 68.4 cm^2 is closest.
96 - y = 161 solve for y
Answer: -65
Step-by-step explanation:
96 - y = 161
-y = 161 - 96
-y = 65
y = -65
Compare: f(x) = 4 and g(x) = 2x2 - 13x + 9
What is the product of their y-intercepts?
It's 36 because f(x)=4 has a y-intercept of 4 and g(x)=2x2-13x+9 has a y-intercept of 9.
Product is a term of muptiplication and 9x4 is 36.
I am giving away points if you answer this Question
What is 2+2